EP2741081B1 - Verfahren zur Schätzung des Vulkanisationsgrads einer Kautschukverbindung - Google Patents

Verfahren zur Schätzung des Vulkanisationsgrads einer Kautschukverbindung Download PDF

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EP2741081B1
EP2741081B1 EP13193307.9A EP13193307A EP2741081B1 EP 2741081 B1 EP2741081 B1 EP 2741081B1 EP 13193307 A EP13193307 A EP 13193307A EP 2741081 B1 EP2741081 B1 EP 2741081B1
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vulcanization
vulcanizing
curve
expression
invariable
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EP2741081A3 (de
EP2741081A2 (de
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Masaya Tsunoda
Arjun Yadav
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Sumitomo Rubber Industries Ltd
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Sumitomo Rubber Industries Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/44—Resins; Plastics; Rubber; Leather
    • G01N33/445—Rubber
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0025—Shearing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0092—Visco-elasticity, solidification, curing, cross-linking degree, vulcanisation or strength properties of semi-solid materials
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/0202—Control of the test
    • G01N2203/0212—Theories, calculations

Definitions

  • the present invention relates to a method for accurately estimating the vulcanization degree of a rubber compound, in particular, a change curve of the vulcanization degree of the rubber compound with vulcanizing time.
  • Non-patent document 1 W.J.TOTH, J.P.CHANG and C.ZANICHELLI, "Finite element evaluation of the state of cure in a tire", Tire Science and Technology: October 1991, vol. 19, No. 4, pp. 178-212 .
  • the non-patent document 1 in order to enable the integration of the expression (3), fixed real numbers are assigned to the invariables m, n and K1, and only the value of the invariable K2 is determined so that the expression (3) becomes close to the actual vulcanization curve as far as possible. Therefore, the method disclosed in the non-patent document 1 has its limit, and the vulcanization degree of the rubber compound can not be accurately estimated.
  • ODR oscillating disc rheometer
  • MDR moving die rheometer
  • DSC differential scanning calorimeter
  • an object of the present invention to provide a method for accurately estimating the vulcanization degree of a rubber compound.
  • the method for estimating the vulcanization degree of a rubber compound according to the present invention can be suitably used for rubber compounds constituting a rubber product such as vehicle tire.
  • Fig. 1 shows a flow chart of the estimating method as an embodiment of the present invention.
  • the shearing resistance or torque of the rubber compound during vulcanization is actually measured to obtain the vulcanization curve (hereinafter the measured vulcanization curve or actual vulcanization curve).
  • the vulcanization curve shows the vulcanization degree X of the rubber compound as a function of the vulcanizing time t.
  • a so called Curelastometer a rubber testing machinery for assessing vulcanization characteristics, is employed.
  • such torque is measured at different vulcanizing temperatures, for example, 150, 160, 170 and 180 degrees C.
  • the measuring conditions are as follows. measuring method: JIS K 6300, Physical Testing Methods
  • the vulcanization degree X of the rubber compound is plotted against the vulcanizing time t to obtain the measured vulcanization curve 2 as shown in Fig. 2 to Fig. 5 .
  • the expression (1) is obtained from the expression (3) explained in the non-patent document 1. 1 (one) is assigned to the invariable n of the expression (3), and the expression (3) is converted to natural logarithm, and then the converted expression is transformed to the expression (1).
  • values of the invariables K1, K2 and m of the expression (1) are determined which values can minimize the error between the measured vulcanization curve 2 and the estimated vulcanization curve 3 which is the curve of the expression (1).
  • Fig. 6 shows a flowchart of the invariable determining process S2 in this embodiment.
  • FIG. 7 A flowchart of this invariable calculating process S21 is shown in Fig. 7 .
  • the lower limit of the real number or the smallest real number is assigned to the invariable K1 of the expression (1).
  • the lower limit of the real number is 1X10 -10 . Therefore, the expression (1) can be transformed into a linear expression whose gradient and intercept are equal to m and K2, respectively.
  • the linear expression transformed from the expression (1) is approximated to the measured vulcanization curve 2 at the vulcanizing temperatures concerned (for example 150 degrees C).
  • the method of least squares is used to approximate the linear expression 4 to the measured vulcanization curve 2 as shown in Fig. 2 .
  • the approximation is possible without complex calculation.
  • the values of the invariables K1, K2 and m thereof are obtained.
  • the invariable K2 and invariable m can be obtained as the gradient and intercept of the approximated linear expression 4.
  • a set of values of the invariables K1, K2 and m, corresponding to the above-mentioned real number assigned to the invariable K1 in the process S211, can be obtained.
  • the current value of the invariable K1 is equal to or more than its upper limit.
  • the upper limit is 1.
  • the real numbers assigned to the invariable K1 are more than 0 and less than 1. If “yes”, then the procedure goes to process S216. If “no” namely the current value of the invariable K1 is less than the upper limit, then the procedure goes to process S215.
  • the invariable K1 is increased to a value equal to the current value multiplied by a predetermined incremental modulus L.
  • the incremental modulus L is 1.1.
  • Fig. 2 only one example of the linear expression 4 approximated to the measured vulcanization curve 2 is shown. But, a plurality of the approximated linear expressions 4 exist corresponding to the real numbers.
  • the linear expression 4 transformed from the expression (1) can be well approximated to the measured vulcanization curve 2. If the real number is more than 1, the degree of the approximation is not increased, and the computational cost is increased.
  • the process S216 it is judged if the above-mentioned plural sets of values of the invariables K1, K2 and m have been obtained with respect to every vulcanizing temperature, in this example, 150, 160, 170 and 180 degrees C. If “yes”, then the procedure goes to a fitted curve determining process S22. If “no”, namely, there exists a vulcanizing temperature about which the plural sets of values of the invariables K1, K2 and m are not yet obtained, then with respect to that vulcanizing temperature, the processes S211 to S216 are repeated.
  • the linear expression 4 is approximated to the measured vulcanization curve 2, and plural sets of values of the invariables K1, K2 and m are obtained.
  • the fitted curve determining process S22 is performed with respect to every vulcanizing temperature.
  • Fig. 8 shows a flowchart of the fitted curve determining process S22 in this embodiment.
  • the process S221 is performed with respect to one of the vulcanizing temperatures.
  • the process S222 is performed with respect to the vulcanizing temperature concerned.
  • an estimated vulcanization curve 3 whose error from the measured vulcanization curve 2 is smallest, namely, most fitted curve 3s is determined or found out.
  • the error between the estimated vulcanization curve 3 and the measured vulcanization curve 2 can be obtained by summing up the difference X1(t)-X2(t) between the vulcanization degree X1(t) of the estimated vulcanization curve 3 at the vulcanizing time t and the vulcanization degree X2(t) of the measured vulcanization curve 2 at the vulcanizing time t from the vulcanizing time t when the vulcanization degree X of the measured vulcanization curve 2 is 0 to the vulcanizing time t when the vulcanization degree X of the measured vulcanization curve 2 is 1.
  • the process S223 it is judged if the most fitted curve 3s has been determined with respect to every vulcanizing temperature for example, 150, 160, 170 and 180 degrees C. If “yes”, then the process S23 goes to process S23. If "no” namely there exists a vulcanizing temperature about which the most fitted curve 3s is not yet determined, then with respect to that vulcanizing temperature, the process S221 to S222 are repeated.
  • the fitted curve determining process S22 the most fitted curves 3s are obtained with respect to all of the vulcanizing temperatures as shown in Fig. 2 to Fig. 5 .
  • the values of the invariables K1, K2 and m can be determined with respect to any vulcanizing temperature s.
  • the most fitted curve 3s (estimated vulcanization curve 3) at any vulcanizing temperature s can be defined easily in a short time in order to accurately estimate the vulcanization degree of the rubber compound.
  • Fig. 10 shows an example of the change curve 7 of the vulcanizing temperature s with the vulcanizing time t as an examination object to be examined as to whether the desired vulcanization degree can be achieved in a process of vulcanizing a rubber compound.
  • Fig. 11 shows a flowchart of the estimating process S3.
  • the vulcanizing temperature s corresponding to a certain point in the vulcanizing time t is obtained from the change curve 7 as shown in Fig. 10 .
  • the obtained vulcanizing temperature s is assigned to the above-mentioned approximate expressions K1(t), K2(t) and m(t), and the values of the invariables K1, K2 and m are obtained therefrom.
  • the obtained values of the invariables K1, K2 and m are assigned to the expression (1), and the gradient (dx/dt) of the vulcanization degree at the certain point in the vulcanizing time t is obtained.
  • the vulcanizing time t is incremented.
  • the vulcanization degree X(t) can be estimated from moment to moment.
  • the obtained vulcanization degree X(t) and the vulcanizing time t are plotted as an estimated vulcanization curve 5.
  • the rubber product is manufactured by vulcanizing a rubber compound according to the change curve 7 as shown in Fig. 10 .
  • the vulcanizing time of a tire is determined by the longest one of the times required for the vulcanization degree X(t) of the rubber members becoming 0.8.
  • the above described method in this embodiment can be suitably used.
  • the measured vulcanization curve of the rubber compound was obtained.
  • the values of invariables K1, K2 and m which minimize the error between the measured vulcanization curve and the estimated vulcanization curve defined by of the expression (1), were obtained.
  • the error (maximum) between the vulcanization degree x(t) of the estimated vulcanization curve obtained by assigning the values of invariables K1, K2 and m and the vulcanization degree X(t) of the measured vulcanization curve was calculated, The results are as follows.
  • the estimated vulcanization curve is considered as being good. In the embodiment 1, therefore, accurate estimated vulcanization curves could be obtained. In other words, the vulcanization degree of the rubber compound at any point in the vulcanizing time t could be accurately estimated.
  • the vulcanization degree or torque was measured according to JIS K 6300, and the change in the vulcanization degree with the vulcanizing time was obtained.
  • an estimated vulcanization curve 5 as shown in Fig. 12 corresponding to the change curve 7 shown in Fig. 10 was obtained.
  • the vulcanizing temperatures were same as those in the embodiment 1.
  • the plural sets of the values for the invariables K1, K2 and m obtained in the embodiment 1 were used.
  • the error (maximum) between the estimated vulcanization curve 5 and the measured change in the vulcanization degree with the vulcanizing time was calculated. As a result, the maximum error was 0.07. If the error is less than 0.1 at any point in the vulcanizing time t, the estimated vulcanization curve is considered as being good. Therefore, the vulcanization degree of the rubber compound at any point in the vulcanizing time t could be accurately estimated.

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  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Engineering & Computer Science (AREA)
  • Food Science & Technology (AREA)
  • Medicinal Chemistry (AREA)
  • Physics & Mathematics (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Heating, Cooling, Or Curing Plastics Or The Like In General (AREA)
  • Tires In General (AREA)

Claims (4)

  1. Verfahren zur Schätzung des Vulkanisationsgrades einer Kautschukmischung, umfassend
    einen Messprozess (S1), in dem eine gemessene Vulkanisationskurve (2), welche eine Änderungskurve des Vulkanisationsgrades der Kautschukmischung über die Vulkanisationszeit ist, dadurch erhalten wird, dass der Scherwiderstand (oder das Drehmoment) der Kautschukmischung während der Vulkanisation tatsächlich gemessen wird,
    einen Konstantenbestimmungsprozess (S2), in dem Werte der Konstanten K1, K2 und m des folgenden Ausdrucks (1) bestimmt werden, welche die Abweichung zwischen der gemessenen Vulkanisationskurve (2) und einer geschätzten Vulkanisationskurve (3) minimieren, die eine Kurve des Ausdrucks (1) ist, ln 1 1 − X dX dt − K 1 = ln K 2 + m ln X
    Figure imgb0012
     wobei
    X: Vulkanisationsgrad
    t: Vulkanisationszeit
    wobei
    der Konstantenbestimmungsprozess (S2) umfasst:
    einen Konstantenberechnungsprozess (S21), in welchem jede von verschiedenen reellen Zahlen der Konstanten K1 des Ausdrucks (1) zugeordnet wird, wobei die reellen Zahlen größer als 0 und kleiner als 1 sind, und ein linearer Ausdruck (4), dessen Gradient und Achsenabschnitt jeweils gleich m und K2 sind, aus dem Ausdruck (1) transformiert und an die gemessene Vulkanisationskurve (2) angenähert wird, und dann aus dem angenäherten Ausdruck ein Satz von Werten für die Konstanten K1, K2 und m erhalten wird,
    wodurch mehrere Sätze von Werten erhalten werden, die den jeweiligen reellen Zahlen entsprechen, und
    einen Bestimmungsprozess für eine angepasste Kurve (S22), in welchem eine Mehrzahl geschätzter Vulkanisationskurven (3) erhalten wird, indem die mehreren Sätze von Werten dem Ausdruck (1) zugeordnet werden, und
    aus einer Mehrzahl der geschätzten Vulkanisationskurven (3) eine geschätzte Vulkanisationskurve 3s ermittelt wird, deren Abweichung von der gemessenen Vulkanisationskurve (2) am geringsten ist.
  2. Verfahren zur Schätzung des Vulkanisationsgrades einer Kautschukmischung gemäß Anspruch 1, wobei
    im Messprozess (S1) die gemessene Vulkanisationskurve (2) hinsichtlich jeder von verschiedenen Vulkanisationstemperaturen erhalten wird, und
    im Bestimmungsprozess für eine angepasste Kurve (S22) für jede der verschiedenen Vulkanisationstemperaturen die geschätzte Vulkanisationskurve (3s) erhalten wird, deren Abweichung von der gemessenen Vulkanisationskurve am geringsten ist.
  3. Verfahren zur Schätzung des Vulkanisationsgrades einer Kautschukmischung gemäß Anspruch 2, wobei der Konstantenbestimmungsprozess (S2) umfasst:
    einen Prozess (S23), in welchem eine Relation zwischen den Werten der Konstanten K1 der geschätzten Vulkanisationskurven, die im Bestimmungsprozess für eine angepasste Kurve (S22) erhalten wurden, und ihren Vulkanisationstemperaturen durch eine Gerade angenähert wird, und der lineare Ausdruck (4) der Geraden als ein näherungsweiser Ausdruck der Konstanten K1 in Relation zur Vulkanisationstemperatur erhalten wird,
    einen Prozess (S24), in welchem eine Relation zwischen den Werten der Konstanten K2 der geschätzten Vulkanisationskurven, die im Bestimmungsprozess für eine angepasste Kurve (S22) erhalten wurden, und ihren Vulkanisationstemperaturen durch eine Gerade angenähert wird und der lineare Ausdruck (4) der Geraden als ein näherungsweiser Ausdruck der Konstanten K2 in Relation zur Vulkanisationstemperatur erhalten wird, und
    einen Prozess (S25), in welchem eine Relation zwischen den Werten der Konstanten m der geschätzten Vulkanisationskurven, die im Bestimmungsprozess für eine angepasste Kurve (S22) erhalten wurden, und ihren Vulkanisationstemperaturen durch eine Gerade angenähert wird und der lineare Ausdruck (4) der Geraden als ein näherungsweiser Ausdruck der Konstanten m in Relation zur Vulkanisationstemperatur erhalten wird.
  4. Verfahren zur Schätzung des Vulkanisationsgrades einer Kautschukmischung gemäß Anspruch 3, welches
    einen Schätzungsprozess (S3) umfasst, in welchem für eine erste Änderungskurve einer Vulkanisationstemperatur über eine Vulkanisationszeit, die dazu ausgelegt ist, die Kautschukmischung zu vulkanisieren, eine zweite Änderungskurve des Vulkanisationsgrades X der Kautschukmischung über die Vulkanisationszeit geschätzt wird,
    wobei der Schätzungsprozess (S3) umfasst:
    einen Prozess, in welchem die Vulkanisationstemperatur, die einem bestimmten Punkt in der Vulkanisationszeit in der ersten Änderungskurve (7) entspricht, dem näherungsweisen Ausdruck der Konstanten K1, dem näherungsweisen Ausdruck der Konstanten K2 und dem näherungsweisen Ausdruck der Konstanten m zugeordnet wird, und
    Werte der Konstanten K1, K2 und m erhalten werden, die dem bestimmten Punkt in der Vulkanisationszeit entsprechen,
    einen Prozess (S32), in welchem die erhaltenen Werte der Konstanten K1, K2 und m, die dem bestimmten Punkt in der Vulkanisationszeit entsprechen, dem Ausdruck (1) zugeordnet werden und der Gradient (dX/dt) des Vulkanisationsgrades an dem bestimmten Punkt in der Vulkanisationszeit erhalten wird, und
    einen Prozess (S33), in welchem durch Zuordnung des erhaltenen Gradienten (dX/dt) zum folgenden Ausdruck (2) und unter Verwendung des Vulkanisationsgrades X(t) an dem bestimmten Punkt in der Vulkanisationszeit der Vulkanisationsgrad X(t+1) nach einer Mikrozeit dt berechnet wird, X t + 1 = X t + dX dt X t t > 0 X 0 = 0
    Figure imgb0013
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CN109900564B (zh) * 2019-03-25 2021-09-28 中国电建集团华东勘测设计研究院有限公司 长大层间错动带摩擦角测量方法
CN112505313A (zh) * 2020-11-02 2021-03-16 中策橡胶集团有限公司 一种橡胶混炼胶加工性能的评价方法
CN112372906B (zh) * 2020-11-18 2021-11-30 清华大学 橡胶件的制备方法、装置、设备和系统
CN113607934B (zh) * 2021-06-18 2023-01-13 中策橡胶集团股份有限公司 一种白炭黑胶料硫化过程评价方法、设备和计算机可读载体介质

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US20140163906A1 (en) 2014-06-12
EP2741081A2 (de) 2014-06-11

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